Abstract
Efficient algorithms are given for decomposing a simple polygon into two special polygons, each with the property that every boundary and interior point can be connected to a single edge by a perpendicular line segment interior to the polygon. This allows efficient construction of certain classes of 3D parts via Layered Manufacturing.
Research of II and RJ supported, in part, by NSF grant CCR-9712226. This effort is also sponsored, in part, by the Army High Performance Computing Research Center under the auspices of the Department of the Army, Army Research Laboratory cooperative agreement number DAAD19-01-2-0014, the content of which does not necessarily reflect the position or the policy of the government, and no official endorsement should be inferred. Research of MS supported by NSERC.
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References
B. Asberg, G. Blanco, P. Bose, J. Garcia-Lopez, M. Overmars, G. Toussaint, G. Wilfong, and B. Zhu. Feasibility of design in stereolithography. Algorithmica, 19:61–83, 1997.
P. Bose, D. Bremner, and M. van Kreveld. Determining the castability of simple polyhedra. Algorithmica, 19(1–2):84–113, Sept. 1997.
S. P. Fekéte and J. S. B. Mitchell. Terrain decomposition and layered manufacturing. Intl. J. Comput. Geom. & Appl., 11:647–668, 2001.
J. Friedman, J. Hershberger, and J. Snoeyink. Efficiently planning compliant motion in the plane. SIAM J. Comput., 25:562–599, 1996.
J. Hershberger and S. Suri. A pedestrian approach to ray shooting: Shoot a ray, take a walk. J. Algorithms, 18:403–431, 1995.
I. Ilinkin, R. Janardan, J. Majhi, J. Schwerdt, M. Smid, and R. Sriram. A decomposition-based approach to layered manufacturing. In Proc. 7th WADS, volume 2125 of LNCS, pages 389–400. Springer-Verlag, 2001. To appear in Comput. Geom. Theory Appl.
I. Ilinkin, R. Janardan, and M. Smid. Terrain polygon decomposition, with application to Layered Manufacturing. http://www.cs.umn.edu/~janardan/terrain.pdf.
C. C. Kai and L. K. Fai. Rapid Prototyping: Principles and Applications in Manufacturing. Wiley and Sons, Inc., 1998.
J. Majhi, R. Janardan, J. Schwerdt, and M. Smid. Multi-criteria optimization algorithms for layered manufacturing. In Proc. 14th Ann. ACM Symp. Comput. Geometry, pages 19–28, 1998. To appear in Intl. J. Math. Algorithms.
J. Majhi, R. Janardan, J. Schwerdt, M. Smid, and P. Gupta. Minimizing support structures and trapped area in two-dimensional layered manufacturing. Comput. Geom. Theory Appl., 12:241–267, 1999.
J. Majhi, R. Janardan, M. Smid, and P. Gupta. On some geometric optimization problems in layered manufacturing. Comput. Geom. Theory Appl., 12:219–239, 1999.
F. Preparata and M. Shamos. Computational Geometry: An Introduction. Springer-Verlag, New York, NY, 1985.
D. Rappaport and A. Rosenbloom. Moldable and castable polygons. Comput. Geom. Theory Appl., 4:219–233, 1994.
G. Toussaint. Solving geometric problems with the rotating calipers. In Proc. IEEE MELECON’ 83, pages A10.02/1–4, 1983.
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Ilinkin, I., Janardan, R., Smid, M. (2002). Terrain Polygon Decomposition, with Application to Layered Manufacturing. In: Ibarra, O.H., Zhang, L. (eds) Computing and Combinatorics. COCOON 2002. Lecture Notes in Computer Science, vol 2387. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45655-4_41
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DOI: https://doi.org/10.1007/3-540-45655-4_41
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